Nonlinear Hydroelastic Analysis Of Viscoelastic Plate

Because of the depletion of land resources,people need to exploit marine resources.The stability of the very large floating structure(VLFS),an important exploitation platform of ocean resources,is related to the safety of operators.The interaction between the VLFS and water waves has been studied by many researches.But most researchers paid their attention to linear problems due to complexity and difficulty of nonlinear questions.So there are few literatures about nonlinear interaction between the VLFS and water waves.The VLFS is usually constructed by steel and concrete,and the steel and concrete show rigidity and elasticity.Therefore,the VLFS is always simulated as an elastic plate or beam on studying the interaction between the VLFS and water waves.However,researchers found that there are errors between theoretical results and experimental results.Subsequent researches show that ignored viscoelasticity of material causes the errors.So the mathematical model with the viscoelastic term can simulate the deflection of the VLFS better.Calculating errors can also be reduced by the mathematical model with the viscoelastic term.Based on above reasons,the hydroelastic respond of the viscoelastic plate at different depths are studied in the paper.We hope that the VLFS can be constructed and maintained better with the help of our conclusions.Main works and results are as follows:(1)The detailed mathematical derivation is carried out for the hydroelastic respond of the viscoelastic plate at infinite depth.The nonlinear problems are transformed into many linear problems which can be solved by the homotopy analysis method(HAM).The accuracy of the calculation can be verified by the log residual error squares.Results show that there are distinct variations for the reflection of the VLFS when the retardation time,wave amplitude,Young’s modulus,the thickness of the plate and the dimensionless parameter change.(2)For the hydroelastic respond of the viscoelastic plate in the finite water depth,the HAM was used to compute the nonlinear problems.The accuracy of the approximate analytical solutions can be verified by the log residual error squares.Because of distinctions between infinite and finite water depth model,different solution experiences and auxiliary linear operators were selected.The residual shows the positive effect of the corrections.Results show that there are obvious variations for the reflection of the VLFS when the retardation time,wave amplitude,water depth,Young’s modulus,the thickness of the plate and the dimensionless parameter change.